Probability | A Time for Reflection

Its that time of year again when the lights are up, songs are being sung, decorations are being hung and joy is absolutely everywhere. What is this time you ask? it is indeed Christmas. It is obvious that Christmas is a time for giving and thinking of loved ones, but after a recent blog post from Andy Hughes (titled ‘Christmaths’), I have been inspired to blog about how maths can be incorporated into Christmas in fun and inventive ways. In addition, it has made me want to uncover the fundamental principles of mathematics in Christmas.

Hughes (2015) in his blog post ‘Christmaths’ describes mathematics in Christmas. He states that snowflake’s are a ‘fractal (a fractal is a shape that contains similar patterns which recur throughout the shape on a smaller scale)’. In addition he identifies that zooming in on a snowflake just produces more details and can splurge up fundamental processes such as scaling, shape and ratio – very fundamental processes. On a larger scale, lets take the fundamental process of shape. As I have mentioned numerous times before, maths is all around us. In a seasonal sense, we only need to look at our Christmas trees to see that shape is evident. For example, Christmas baubles. These are spherical in shape. The star on top of the tree also shines bright, but is still a shape. However, what is the maths behind a Christmas tree? It could be suggested that there is maths in assembling a Christmas tree (especially and artificial one. For example, you will need to have the right length of Christmas tinsel to pass around the tree – the mathematical concept of length and measurement. In addition, you will need to have enough Christmas baubles in order for the tree to be symmetrical. Talking about symmetry, this can be used widely as examples to help children understand this concept. For example, trees are symmetrical, as are snowmen, stars, snowflakes.. the list goes on. This can be used as a consolidation activity and it effectively ties Christmas into mathematics.

Moreover, Christmas time in the classroom should be an exciting and engaging time for children. So why can’t we use maths within Christmas? Even if it is not directly from a maths lesson. Board games are a fantastic way to do this and they challenge a range of mathematical concepts. Take monopoly, for example. Now, I am not going to lecture you on how to play monopoly as I am sure we all have a ‘profound understanding’ of how to play it. However, what does monopoly all boil down to? Money. In order to play this game, children must have a basic knowledge of money and will have to subtract or add together money when they land on someone’s property or even if they pass go! I find this to be pretty incredible – its fun and engaging, but you are learning at the same time… Do you see where I am going with this? Take snakes and ladders – counting is the fundamental principle there. Cluedo – problem solving to find out who really committed the crime. Even in dominos there is a basic element of counting. Probability is also another fundamental principle that can be seen in games that use dice – what is the probability of landing on a six? Lets be honest, which games do not have dice in them?

It is obviously apparent that maths is incorporated into Christmas profoundly. If you even think about presents under your tree – some are cuboidal and some are spherical. Shape is such a common theme within Christmas. So when your opening your presents this year, have a second thought about how maths is incorporated into Christmas – it may even inspire you to write a blog post!!!!

reference:

Hughes, A. (2015) Christmaths. In a Class of my Own. Last accessed 06/12/15. Available at https://blogs.glowscotland.org.uk/glowblogs/ajhportfolio/2015/12/02/christmaths/

After all this hype about a potentially menacing storm that has hit the shores of Scotland, I thought to myself that it couldn’t actually be that bad. I was, however, mistaken to this notion. After walking along Dundee City high street a few moments ago, I was soaked within an inch of my life. It was calm one minute, then BOOM chaos! The storm has now come to Dundee and as I look out my window now, Dundee has been disrupted with small amounts of damage to public billboards and bus shelters. This got me thinking about the intensity of a storm and how vast they can be. It also got me thinking about how the maths come in to part with storms. As I sit with a blanket over my lap and a cup of tea by my side, I am going to attempt to discover the fundamental maths behind a hurricane and why they can be incredibly frustrating for everyone.

In my last few blog posts, I have been concerned with talking about maths as an active subject through many things like tessellation and maths with stories and play. This blog post will be somewhat different to these, but the principles and the fundamental mathematics still apply. Firstly, a hurricane is a mass storm with a violent wind and reaches above a speed of 75 mph!! 75 miles per hour… I don’t know what is scarier, the damage that it causes or the notion that it can travel faster than the speed limit of a car on the motorway. According to NASA (undated), Hurricanes are like giant engines that use warm, moist air as fuel. That is why they form only over warm ocean waters near the equator. The warm, moist air over the ocean rises upward from near the surface. Because this air moves up and away from the surface, there is less air left near the surface. Another way to say the same thing is that the warm air rises, causing an area of lower air pressure below. NASA continue by suggesting that air from surrounding areas with higher air pressure pushes in to the low pressure area. Then that “new” air becomes warm and moist and rises, too. As the warm air continues to rise, the surrounding air swirls in to take its place. As the warmed, moist air rises and cools off, the water in the air forms clouds. The whole system of clouds and wind spins and grows, fed by the ocean’s heat and water evaporating from the surface. In addition, a hurricane has an abundance of cumulonimbus clouds that form circular bands. The fundamental mathematics of a hurricane is its circular formation. Not only this, it is astonishing the way that hurricanes actually rotate. Do they rotate clockwise, or anticlockwise? storms from the north of the equator spin anti-clockwise and storms below the equator spin clockwise. This is because the Earth rotates on its axis. I find that so absolutely fascinating to say the least. It ultimately highlights that Mathematics is incorporated into absolutely everything that we see in this world and I agree with Will Berry on that one after his lecture on maths in the outdoors.

So why does this leave me feeling fascinated? Well probably because I am thinking about the mathematical activities that you could do within the context of the classroom. Firstly, you could investigate and display the different levels a hurricane is classified as. See diagram below:

Category	Wind Speed (mph)	Damage at Landfall	Storm Surge (feet)
1	74-95	Minimal	4-5
2	96-110	Moderate	6-8
3	111-130	Extensive	9-12
4	131-155	Extreme	13-18
5	Over 155	Catastrophic	19+

The children can ultimately collect the data to classify different (old or new storms) from around the world, especially in the case of hurricane Abigail. In addition, the children could also find the speed of the hurricane and predict how far it will travel and in what time by using the speed, distance, time formula. This is just naming a few, but please feel free to comment with any other activities that you can think of as I would like to read them.

Fundamentally, the basic maths behind an activity to do with a hurricane is research skills. Being able to tally, collect data and the general notion of handling and organising information. Not only this, this is good for children deepen their understanding of probability and likelihood of a storm like this happening again. The activities can be in abundance if you put your mind to it.

Finally, I will leave you with this satellite image of hurricane Abigail (picture taken by the University of Dundee):

Storm Abigail

This is a picture of hurricane Abigail just off the coast of North West Scotland. You can see the spiral motion and you can almost imagine the wind swishing and swaying around. What I find to be completely fascinating about this picture is that you can see Fibonacci’s sequence spiralling around and around (see image below):

Mathematics… You have amazed me again.

Christmas in Mathematics – ideas for the classroom

The Maths Behind Hurricane Abigail